Problem: Simplify the following expression: $n = \dfrac{y^2 + 4y + 3}{y + 1} $
First factor the polynomial in the numerator. $ y^2 + 4y + 3 = (y + 1)(y + 3) $ So we can rewrite the expression as: $n = \dfrac{(y + 1)(y + 3)}{y + 1} $ We can divide the numerator and denominator by $(y + 1)$ on condition that $y \neq -1$ Therefore $n = y + 3; y \neq -1$